2,031 research outputs found
Testing for Homogeneity with Kernel Fisher Discriminant Analysis
We propose to investigate test statistics for testing homogeneity in
reproducing kernel Hilbert spaces. Asymptotic null distributions under null
hypothesis are derived, and consistency against fixed and local alternatives is
assessed. Finally, experimental evidence of the performance of the proposed
approach on both artificial data and a speaker verification task is provided
Parsimonious Kernel Fisher Discrimination
By applying recent results in optimization transfer, a new algorithm for kernel Fisher Discriminant Analysis is provided that makes use of a non-smooth penalty on the coefficients to provide a parsimonious solution. The algorithm is simple, easily programmed and is shown to perform as well as or better than a number of leading machine learning algorithms on a substantial benchmark. It is then applied to a set of extreme small-sample-size problems in virtual screening where it is found to be less accurate than a currently leading approach but is still comparable in a number of cases
Fast Two-Sample Testing with Analytic Representations of Probability Measures
We propose a class of nonparametric two-sample tests with a cost linear in
the sample size. Two tests are given, both based on an ensemble of distances
between analytic functions representing each of the distributions. The first
test uses smoothed empirical characteristic functions to represent the
distributions, the second uses distribution embeddings in a reproducing kernel
Hilbert space. Analyticity implies that differences in the distributions may be
detected almost surely at a finite number of randomly chosen
locations/frequencies. The new tests are consistent against a larger class of
alternatives than the previous linear-time tests based on the (non-smoothed)
empirical characteristic functions, while being much faster than the current
state-of-the-art quadratic-time kernel-based or energy distance-based tests.
Experiments on artificial benchmarks and on challenging real-world testing
problems demonstrate that our tests give a better power/time tradeoff than
competing approaches, and in some cases, better outright power than even the
most expensive quadratic-time tests. This performance advantage is retained
even in high dimensions, and in cases where the difference in distributions is
not observable with low order statistics
Wavelet Features for Recognition of First Episode of Schizophrenia from MRI Brain Images
Machine learning methods are increasingly used in various fields of medicine, contributing to early diagnosis and better quality of care. These outputs are particularly desirable in case of neuropsychiatric disorders, such as schizophrenia, due to the inherent potential for creating a new gold standard in the diagnosis and differentiation of particular disorders. This paper presents a scheme for automated classification from magnetic resonance images based on multiresolution representation in the wavelet domain. Implementation of the proposed algorithm, utilizing support vector machines classifier, is introduced and tested on a dataset containing 104 patients with first episode schizophrenia and healthy volunteers. Optimal parameters of different phases of the algorithm are sought and the quality of classification is estimated by robust cross validation techniques. Values of accuracy, sensitivity and specificity over 71% are achieved
Operators for transforming kernels into quasi-local kernels that improve SVM accuracy
Motivated by the crucial role that locality plays in various learning approaches, we present, in the framework of kernel machines for classification, a novel family of operators on kernels able to integrate local information into any kernel obtaining quasi-local kernels. The quasi-local kernels maintain the possibly global properties of the input kernel and they increase the kernel value as the points get closer in the feature space of the input kernel, mixing the effect of the input kernel with a kernel which is local in the feature space of the input one. If applied on a local kernel the operators introduce an additional level of locality equivalent to use a local kernel with non-stationary kernel width. The operators accept two parameters that regulate the width of the exponential influence of points in the locality-dependent component and the balancing between the feature-space local component and the input kernel. We address the choice of these parameters with a data-dependent strategy. Experiments carried out with SVM applying the operators on traditional kernel functions on a total of 43 datasets with diÂźerent characteristics and application domains, achieve very good results supported by statistical significance
Recent advances in directional statistics
Mainstream statistical methodology is generally applicable to data observed
in Euclidean space. There are, however, numerous contexts of considerable
scientific interest in which the natural supports for the data under
consideration are Riemannian manifolds like the unit circle, torus, sphere and
their extensions. Typically, such data can be represented using one or more
directions, and directional statistics is the branch of statistics that deals
with their analysis. In this paper we provide a review of the many recent
developments in the field since the publication of Mardia and Jupp (1999),
still the most comprehensive text on directional statistics. Many of those
developments have been stimulated by interesting applications in fields as
diverse as astronomy, medicine, genetics, neurology, aeronautics, acoustics,
image analysis, text mining, environmetrics, and machine learning. We begin by
considering developments for the exploratory analysis of directional data
before progressing to distributional models, general approaches to inference,
hypothesis testing, regression, nonparametric curve estimation, methods for
dimension reduction, classification and clustering, and the modelling of time
series, spatial and spatio-temporal data. An overview of currently available
software for analysing directional data is also provided, and potential future
developments discussed.Comment: 61 page
Nonparametric Detection of Anomalous Data Streams
A nonparametric anomalous hypothesis testing problem is investigated, in
which there are totally n sequences with s anomalous sequences to be detected.
Each typical sequence contains m independent and identically distributed
(i.i.d.) samples drawn from a distribution p, whereas each anomalous sequence
contains m i.i.d. samples drawn from a distribution q that is distinct from p.
The distributions p and q are assumed to be unknown in advance.
Distribution-free tests are constructed using maximum mean discrepancy as the
metric, which is based on mean embeddings of distributions into a reproducing
kernel Hilbert space. The probability of error is bounded as a function of the
sample size m, the number s of anomalous sequences and the number n of
sequences. It is then shown that with s known, the constructed test is
exponentially consistent if m is greater than a constant factor of log n, for
any p and q, whereas with s unknown, m should has an order strictly greater
than log n. Furthermore, it is shown that no test can be consistent for
arbitrary p and q if m is less than a constant factor of log n, thus the
order-level optimality of the proposed test is established. Numerical results
are provided to demonstrate that our tests outperform (or perform as well as)
the tests based on other competitive approaches under various cases.Comment: Submitted to IEEE Transactions on Signal Processing, 201
Kernel-Based Methods for Hypothesis Testing: A Unified View
International audienceKernel-based methods provide a rich and elegant framework for developing nonparametric detection procedures for signal processing. Several recently proposed procedures can be simply described using basic concepts of reproducing kernel Hilbert space embeddings of probability distributions, namely mean elements and covariance operators. We propose a uniïŹed view of these tools, and draw relationships with information divergences between distributions
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